Which of the following numbers is a factor of 55? ${4,6,10,11,13}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $55$ by each of our answer choices. $55 \div 4 = 13\text{ R }3$ $55 \div 6 = 9\text{ R }1$ $55 \div 10 = 5\text{ R }5$ $55 \div 11 = 5$ $55 \div 13 = 4\text{ R }3$ The only answer choice that divides into $55$ with no remainder is $11$ $ 5$ $11$ $55$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $11$ are contained within the prime factors of $55$ $55 = 5\times11 11 = 11$ Therefore the only factor of $55$ out of our choices is $11$. We can say that $55$ is divisible by $11$.